Financial Time Series Forecasting Using an ARMA-CNNLSTM Deep Ensemble

Abstract

Accurate financial time series forecasting remains difficult because asset prices often exhibit both linear dependence and nonlinear dynamics. This paper proposes an ARMA-CNNLSTM deep ensemble for this setting. The framework combines an autoregressive moving average (ARMA) model for linear autocorrelation with a CNN-LSTM network for nonlinear spatiotemporal feature extraction and aggregates the two prediction streams through simple averaging. The model is evaluated on three representative financial series, namely weekly EU ETS prices, daily Shanghai Stock Exchange Composite Index data, and daily Bitcoin prices. Its performance is compared with random walk, ARMA, multi-layer perceptron, CNN, and LSTM benchmarks using RMSE, MAPE, MAE, and directional statistics. Across the datasets considered here, the proposed model shows the most favorable overall out-of-sample performance, especially when numerical and directional accuracy are considered jointly. These results support the use of separate linear and nonlinear learners in financial time series forecasting.